Spotting symmetry in the skyscrapers

Cities are geometrical, engineered sort of places. No surprise, then, that cities the world over speak the same language: mathematics.

It’s a point that University of Oxford professor Marcus du Sautoy drives home admirably in the mathematical walking tour of London that he and his team of Oxford student “mathemagicians” have devised.

The tour is part of the “Maths in the City” initiative fronted by du Sautoy. On its website you can upload your own examples of urban maths: a quick browse reveals, for instance, that pi is defined on the walls of a subway station in Vienna, Austria, or that Albuquerque, New Mexico, is the self-styled “fractal capital of the world”.

The London tour follows one running in Oxford since last year. It starts with an exposition of the most famous mathematical walking tour: the “Bridges of Königsberg” problem, which asked whether it was possible to cross each of the seven bridges in the Prussian city once and only once. Leonhard Euler’s 1735 proof that you couldn’t laid the ground work for graph theory, which today underpins our understanding of social, financial and other all-important networks.

No such problems with the London walk, which crosses just one bridge on its route from the Tate Modern art gallery on the south bank of the Thames to St Paul’s cathedral on the north side. It is the Millennium Bridge, the notorious “bridge of sways” whose unexpected shakiness in the face of a pedestrian onslaught caused it to be closed for a hasty engineering upgrade just days after it opened in 2000. With the aid of pendulums and a piece of string, du Sautoy explains how the initial natural, regular swaying of the bridge caused walkers to walk in lock-step at the same frequency, amplifying the sway and setting in train a positive feedback process that rapidly got out of control.

And that’s the beauty of the tour: du Sautoy is a hands-on sort of chap, and says he wanted to avoid a plaque-and-talk sort of tour based exclusively on accounts of historical worthies. Future walks will be guided by his mathemagicians, but participants can still expect to get their hands dirty - whether building geometrical shapes out of canes to compare their stability or, in my case, getting tied hopelessly in knots to illustrate the twists of topology.